An infinite horizontal string is plucked. The vertical displacement of the string is the solutionto the following initial value problemx E R, t > 0u(x,0) = ¢(x)ди(x, 0) = 0Ətwith[- |x|/2, for x|< 2O(x) =0,for |x| > 2(i) Using d'Alembert's solution, give an explicit solution to this initial value problem.

This problem can be solved using the D'Alembert formula for the solution of wave equation.

An infinite horizontal string is plucked. The vertical displacement of the string is the solution to the following initial value problem x E R, t > 0 u(x, 0) = $(x) ди (x, 0) = 0 with 1- |æ|/2, for |x| < 2 $(x) = for |x| > 2 (i) Using d'Alembert's solution, give an explicit solution to this initial value problem.

An infinite horizontal string is plucked. The vertical displacement of the string is the solution to the following initial value problem x E R, t > 0 u(x, 0) = $(x) ди (x, 0) = 0 with 1- |æ|/2, for |x| < 2 $(x) = for |x| > 2 (i) Using d'Alembert's solution, give an explicit solution to this initial value problem.